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QUESTION: 1

Which of the following is the unit of angular acceleration?

Solution:

Angular acceleration is the rate of change of angular velocity. In three dimensions, it is a pseudo-vector. In SI units, it is measured in radians per second squared (rad/s2), and is usually denoted by the Greek letter alpha (α).

QUESTION: 2

Which of the following statements give the relationship between linear velocity and angular velocity correctly?

Solution:

Linear velocity (V) = angular velocity (w) × radius (r)

v = w × r

w = v/r

QUESTION: 3

The angular velocity of the second hand of a clock is :

Solution:

Second’s hand of a clock completes one turn in one second.i.e 1 revolution per minute

Angular velocity of second’s hand;

ω = 2π/60 = π/30 rad/s

QUESTION: 4

Vectorially, angular velocity of a rotating body is represented :

Solution:

Angular velocity is a pseudovector , with its magnitude measuring the rate of rotation and its direction pointing along the axis of rotation ( perpendicular to radius and velocity vectors ) .

QUESTION: 5

A man standing on a table rotating about the central axis pulls his hands holding the dumb bells towards chest. How the angular velocity will change?

Solution:

When the man pulls his hands towards chest, the moment of inertia will decrease and due to conservation of angular momentum, angular velocity will increase.

QUESTION: 6

Angle of line relative to a fixed direction is

Solution:

Angle of line relative to a fixed direction is angular position.

QUESTION: 7

A body is moving with a constant speed v in a circle of radius r. What is the angular acceleration?

Solution:

When a body performs circular motion it has got two accelerations radial acc. And tangential acc. Radial acc. Is responsible for changing the direction of velocity of body but tangential acc. Is responsible for changing the magnitide of velocity of body. As the body is moving with constant speed so tangential acc. Is zero. As we know that tangential acc. = radius * angular acc. So angular acc.is zero.

QUESTION: 8

What is the number of instantaneous centres of rotation for a 6-link mechanism?

Solution:

N = n(n – 1)/2 = 6 x (6 – 1)/2 = 15.

QUESTION: 9

Four billiards balls, each of mass 0.5 kg, all are travelling in the same direction on a billiard table, with speeds of 2 m/s, 4 m/s, 8 m/s and 10 m/s. What is the linear momentum of this system?

Solution:

As the direction of all the four velocities are the same thus their momentum also have same directions and hence they can be directly added.

Thus total momentum of the system, P = 0.5 x 2 + 0.5 x 4 + 0.5 x 8 + 0.5 x 10

= 1 + 2 + 4 + 5

= 12 kg m /sec

QUESTION: 10

Which of the following relations is wrong?

Solution:

Just like the equations of motion in 1D, we get the equations of motion for rotation.

We know that s = d/t, analogous to it is

Hence D is the correct answer.

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